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04 May 2017, 01:53
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
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Question Stats:
92% (01:36) correct
8%
(02:01)
wrong
based on 70
sessions
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Date
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Not Attempted Yet
On one exam, the average (arithmetic mean) in a class of 20 students was 80%. A week later, a new student enrolled in the class, and had to make up this exam. If the average on the exam for the class increases to 80.5%, what grade did the new student receive on his exam?
A. 90.5
B. 89
C. 85.5
D. 82
E. 80.5
A. 90.5
B. 89
C. 85.5
D. 82
E. 80.5
04 May 2017, 03:54
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Here is a technique I learned from one of the post by VeritasPrepKarishma ma’am :
Mean of 20 People = 80
Mean of 21 People = 80.5
Difference = 0.5 (meaning : addition of one person’s score increases the mean by 0.5)
So the new person will have to contribute = 80.5
Additionally, the new person will have to contribute 0.5 on behalf of the other 20 people to raise the mean by 0.5 ..thus 20 x 0.5 = 10
So total contribution by new people = 10 + 80.5 = 90.5
So, answer = A
Mean of 20 People = 80
Mean of 21 People = 80.5
Difference = 0.5 (meaning : addition of one person’s score increases the mean by 0.5)
So the new person will have to contribute = 80.5
Additionally, the new person will have to contribute 0.5 on behalf of the other 20 people to raise the mean by 0.5 ..thus 20 x 0.5 = 10
So total contribution by new people = 10 + 80.5 = 90.5
So, answer = A
WiziusCareers1
Joined: 27 Apr 2009
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GMAT 1: 730 Q51 V36
04 May 2017, 06:08
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Approach 1:
Let the total score of the test = 100
=> The 20 students scored a total of 20*80 = 1600
When the new student attempted the test, the new average is 80.5.
=> The 21 students scored a total of 21*80.5 = 1690.5
So, the new student scored 1690.5 - 1690 = 90.5
Approach 2:
The new student has to contribute 80.5 (this is the average) + he has to contribute 0.5 more to each of the 20 students = 80.5 + (0.5*20) = 90.5
Let the total score of the test = 100
=> The 20 students scored a total of 20*80 = 1600
When the new student attempted the test, the new average is 80.5.
=> The 21 students scored a total of 21*80.5 = 1690.5
So, the new student scored 1690.5 - 1690 = 90.5
Approach 2:
The new student has to contribute 80.5 (this is the average) + he has to contribute 0.5 more to each of the 20 students = 80.5 + (0.5*20) = 90.5
